Given $ m \angle AOB = 7x - 33$, and $ m \angle BOC = 5x + 33$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Solution: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {7x - 33} + {5x + 33} = {180}$ Combine like terms: $ 12x + 0 = 180$ Add $0$ to both sides: $ 12x = 180$ Divide both sides by $12$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 5({15}) + 33$ Simplify: $ {m\angle BOC = 75 + 33}$ So ${m\angle BOC = 108}$.